On Sampling Edges Almost Uniformly

Authors Talya Eden, Will Rosenbaum

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Talya Eden
Will Rosenbaum

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Talya Eden and Will Rosenbaum. On Sampling Edges Almost Uniformly. In 1st Symposium on Simplicity in Algorithms (SOSA 2018). Open Access Series in Informatics (OASIcs), Volume 61, pp. 7:1-7:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We consider the problem of sampling an edge almost uniformly from an unknown graph, G = (V, E). Access to the graph is provided via queries of the following types: (1) uniform vertex queries, (2) degree queries, and (3) neighbor queries. We describe a new simple algorithm that returns a random edge e in E using \tilde{O}(n/sqrt{eps m}) queries in expectation, such that each edge e is sampled with probability (1 +/- eps)/m. Here, n = |V| is the number of vertices, and m = |E| is the number of edges. Our algorithm is optimal in the sense that any algorithm that samples an edge from an almost-uniform distribution must perform Omega(n/sqrt{m}) queries.
  • Sublinear Algorithms
  • Graph Algorithms
  • Sampling Edges
  • Query Complexity


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  1. Talya Eden, Amit Levi, Dana Ron, and C. Seshadhri. Approximately counting triangles in sublinear time. SIAM J. Comput., 46(5):1603-1646, 2017. URL: http://dx.doi.org/10.1137/15M1054389.
  2. Talya Eden, Dana Ron, and C. Seshadhri. Sublinear time estimation of degree distribution moments: The degeneracy connection. In Ioannis Chatzigiannakis, Piotr Indyk, Fabian Kuhn, and Anca Muscholl, editors, 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017, July 10-14, 2017, Warsaw, Poland, volume 80 of LIPIcs, pages 7:1-7:13. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2017. URL: http://dx.doi.org/10.4230/LIPIcs.ICALP.2017.7.
  3. Talya Eden and Will Rosenbaum. On sampling edges almost uniformly. CoRR, abs/1706.09748, 2017. URL: http://arxiv.org/abs/1706.09748.
  4. Uriel Feige. On sums of independent random variables with unbounded variance and estimating the average degree in a graph. SIAM J. Comput., 35(4):964-984, 2006. URL: http://dx.doi.org/10.1137/S0097539704447304.
  5. Oded Goldreich and Dana Ron. Property testing in bounded degree graphs. In Frank Thomson Leighton and Peter W. Shor, editors, Proceedings of the Twenty-Ninth Annual ACM Symposium on the Theory of Computing, El Paso, Texas, USA, May 4-6, 1997, pages 406-415. ACM, 1997. URL: http://dx.doi.org/10.1145/258533.258627.
  6. Oded Goldreich and Dana Ron. Approximating average parameters of graphs. Random Struct. Algorithms, 32(4):473-493, 2008. URL: http://dx.doi.org/10.1002/rsa.20203.
  7. Tali Kaufman, Michael Krivelevich, and Dana Ron. Tight bounds for testing bipartiteness in general graphs. SIAM J. Comput., 33(6):1441-1483, 2004. URL: http://dx.doi.org/10.1137/S0097539703436424.
  8. Michal Parnas and Dana Ron. Testing the diameter of graphs. Random Struct. Algorithms, 20(2):165-183, 2002. URL: http://dx.doi.org/10.1002/rsa.10013.
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